%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP151^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:04:31 AM UTC 2026
% Result : Theorem 1.11s 0.48s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 31 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 100 ( 23 ~; 10 |; 1 &; 62 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 24 !; 1 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
int: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_sort3,type,
polyno727731844poly_a: $tType ).
thf(decl_25,type,
zero_zero_int: int ).
thf(decl_26,type,
zero_zero_nat: nat ).
thf(decl_27,type,
suc: nat > nat ).
thf(decl_28,type,
semiri2019852685at_int: nat > int ).
thf(decl_31,type,
ord_less_nat: nat > nat > $o ).
thf(decl_34,type,
polyno578545843gree_a: polyno727731844poly_a > nat ).
thf(decl_37,type,
polyno1372495879olyh_a: polyno727731844poly_a > nat > $o ).
thf(decl_40,type,
n: nat ).
thf(decl_41,type,
p: polyno727731844poly_a ).
thf(decl_45,type,
esk4_1: nat > nat ).
thf(decl_74,type,
esk33_1: nat > nat ).
thf(fact_55_of__nat__neq__0,axiom,
! [X1: nat] :
( ( semiri2019852685at_int @ ( suc @ X1 ) )
!= zero_zero_int ),
file('/export/starexec/sandbox/tmp/tmp.ykrkiHCEqq/E---3.1_1783062.p',fact_55_of__nat__neq__0) ).
thf(fact_56_polypow_Ocases,axiom,
! [X7: nat] :
( ( X7 != zero_zero_nat )
=> ~ ! [X23: nat] :
( X7
!= ( suc @ X23 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ykrkiHCEqq/E---3.1_1783062.p',fact_56_polypow_Ocases) ).
thf(conj_2,conjecture,
( ( polyno578545843gree_a @ p )
= zero_zero_nat ),
file('/export/starexec/sandbox/tmp/tmp.ykrkiHCEqq/E---3.1_1783062.p',conj_2) ).
thf(fact_98_gr0__conv__Suc,axiom,
! [X1: nat] :
( ( ord_less_nat @ zero_zero_nat @ X1 )
<=> ? [X42: nat] :
( X1
= ( suc @ X42 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ykrkiHCEqq/E---3.1_1783062.p',fact_98_gr0__conv__Suc) ).
thf(fact_31_degree__isnpolyh__Suc,axiom,
! [X13: polyno727731844poly_a,X1: nat] :
( ( polyno1372495879olyh_a @ X13 @ ( suc @ X1 ) )
=> ( ( polyno578545843gree_a @ X13 )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.ykrkiHCEqq/E---3.1_1783062.p',fact_31_degree__isnpolyh__Suc) ).
thf(conj_0,hypothesis,
ord_less_nat @ zero_zero_nat @ n,
file('/export/starexec/sandbox/tmp/tmp.ykrkiHCEqq/E---3.1_1783062.p',conj_0) ).
thf(conj_1,hypothesis,
polyno1372495879olyh_a @ p @ n,
file('/export/starexec/sandbox/tmp/tmp.ykrkiHCEqq/E---3.1_1783062.p',conj_1) ).
thf(fact_43_of__nat__0,axiom,
( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox/tmp/tmp.ykrkiHCEqq/E---3.1_1783062.p',fact_43_of__nat__0) ).
thf(c_0_8,plain,
! [X1: nat] :
( ( semiri2019852685at_int @ ( suc @ X1 ) )
!= zero_zero_int ),
inference(fof_simplification,[status(thm)],[fact_55_of__nat__neq__0]) ).
thf(c_0_9,plain,
! [X7: nat] :
( ( X7 != zero_zero_nat )
=> ~ ! [X23: nat] :
( X7
!= ( suc @ X23 ) ) ),
inference(fof_simplification,[status(thm)],[fact_56_polypow_Ocases]) ).
thf(c_0_10,negated_conjecture,
( ( polyno578545843gree_a @ p )
!= zero_zero_nat ),
inference(assume_negation,[status(cth)],[conj_2]) ).
thf(c_0_11,plain,
! [X1344: nat] :
( ( semiri2019852685at_int @ ( suc @ X1344 ) )
!= zero_zero_int ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).
thf(c_0_12,plain,
! [X1474: nat,X1476: nat,X1477: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ X1474 )
| ( X1474
= ( suc @ ( esk33_1 @ X1474 ) ) ) )
& ( ( X1476
!= ( suc @ X1477 ) )
| ( ord_less_nat @ zero_zero_nat @ X1476 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_98_gr0__conv__Suc])])])])])]) ).
thf(c_0_13,plain,
! [X1311: polyno727731844poly_a,X1312: nat] :
( ~ ( polyno1372495879olyh_a @ X1311 @ ( suc @ X1312 ) )
| ( ( polyno578545843gree_a @ X1311 )
= zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_31_degree__isnpolyh__Suc])])]) ).
thf(c_0_14,plain,
! [X1345: nat] :
( ( X1345 = zero_zero_nat )
| ( X1345
= ( suc @ ( esk4_1 @ X1345 ) ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
thf(c_0_15,negated_conjecture,
( ( polyno578545843gree_a @ p )
!= zero_zero_nat ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
! [X1: nat] :
( ( semiri2019852685at_int @ ( suc @ X1 ) )
!= zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,plain,
! [X1: nat] :
( ( X1
= ( suc @ ( esk33_1 @ X1 ) ) )
| ~ ( ord_less_nat @ zero_zero_nat @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
! [X12: polyno727731844poly_a,X1: nat] :
( ( ( polyno578545843gree_a @ X12 )
= zero_zero_nat )
| ~ ( polyno1372495879olyh_a @ X12 @ ( suc @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,plain,
! [X1: nat] :
( ( X1 = zero_zero_nat )
| ( X1
= ( suc @ ( esk4_1 @ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,negated_conjecture,
( ( polyno578545843gree_a @ p )
!= zero_zero_nat ),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
thf(c_0_21,plain,
! [X1: nat] :
( ( ( semiri2019852685at_int @ X1 )
!= zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ X1 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_22,hypothesis,
ord_less_nat @ zero_zero_nat @ n,
inference(split_conjunct,[status(thm)],[conj_0]) ).
thf(c_0_23,plain,
! [X12: polyno727731844poly_a,X1: nat] :
( ( ( polyno578545843gree_a @ X12 )
= zero_zero_nat )
| ( X1 = zero_zero_nat )
| ~ ( polyno1372495879olyh_a @ X12 @ X1 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_24,hypothesis,
polyno1372495879olyh_a @ p @ n,
inference(split_conjunct,[status(thm)],[conj_1]) ).
thf(c_0_25,negated_conjecture,
( ( polyno578545843gree_a @ p )
!= zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,hypothesis,
( ( semiri2019852685at_int @ n )
!= zero_zero_int ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_27,hypothesis,
n = zero_zero_nat,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
thf(c_0_28,plain,
( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int ),
inference(split_conjunct,[status(thm)],[fact_43_of__nat__0]) ).
thf(c_0_29,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP151^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n002.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 20:04:52 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.22/0.28 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.ykrkiHCEqq/E---3.1_1783062.p
% 1.11/0.48 % Version: 3.5.1-ho
% 1.11/0.48 % Preprocessing class: HSLSSMSSSSSNHFA.
% 1.11/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.48 % Starting new_ho_10 with 1500s (5) cores
% 1.11/0.48 % Starting new_ho_10_unif with 300s (1) cores
% 1.11/0.48 % Starting sh10 with 300s (1) cores
% 1.11/0.48 % Starting lpo5_rw_fix with 300s (1) cores
% 1.11/0.48 % new_ho_10 with pid 1783102 completed with status 0
% 1.11/0.48 % Result found by new_ho_10
% 1.11/0.48 % Preprocessing class: HSLSSMSSSSSNHFA.
% 1.11/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.48 % Starting new_ho_10 with 1500s (5) cores
% 1.11/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.11/0.48 % No SInE strategy applied
% 1.11/0.48 % Search class: HGHSM-FSLM32-MHFFFSBC
% 1.11/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.11/0.48 % Starting SubtermCWHack with 136s (1) cores
% 1.11/0.48 % Starting new_ho_10 with 151s (1) cores
% 1.11/0.48 % Starting lpo6_lambda_fix with 136s (1) cores
% 1.11/0.48 % Starting new_ho_3 with 136s (1) cores
% 1.11/0.48 % Starting sh3 with 136s (1) cores
% 1.11/0.48 % new_ho_10 with pid 1783121 completed with status 0
% 1.11/0.48 % Result found by new_ho_10
% 1.11/0.48 % Preprocessing class: HSLSSMSSSSSNHFA.
% 1.11/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.48 % Starting new_ho_10 with 1500s (5) cores
% 1.11/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.11/0.48 % No SInE strategy applied
% 1.11/0.48 % Search class: HGHSM-FSLM32-MHFFFSBC
% 1.11/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.11/0.48 % Starting SubtermCWHack with 136s (1) cores
% 1.11/0.48 % Starting new_ho_10 with 151s (1) cores
% 1.11/0.48 % Preprocessing time : 0.007 s
% 1.11/0.48 % Presaturation interreduction done
% 1.11/0.48
% 1.11/0.48 % Proof found!
% 1.11/0.48 % SZS status Theorem
% 1.11/0.48 % SZS output start CNFRefutation
% See solution above
% 1.11/0.48 % Parsed axioms : 373
% 1.11/0.48 % Removed by relevancy pruning/SinE : 0
% 1.11/0.48 % Initial clauses : 712
% 1.11/0.48 % Removed in clause preprocessing : 47
% 1.11/0.48 % Initial clauses in saturation : 665
% 1.11/0.48 % Processed clauses : 1306
% 1.11/0.48 % ...of these trivial : 23
% 1.11/0.48 % ...subsumed : 448
% 1.11/0.48 % ...remaining for further processing : 835
% 1.11/0.48 % Other redundant clauses eliminated : 147
% 1.11/0.48 % Clauses deleted for lack of memory : 0
% 1.11/0.48 % Backward-subsumed : 2
% 1.11/0.48 % Backward-rewritten : 15
% 1.11/0.48 % Generated clauses : 4268
% 1.11/0.48 % ...of the previous two non-redundant : 3723
% 1.11/0.48 % ...aggressively subsumed : 0
% 1.11/0.48 % Contextual simplify-reflections : 1
% 1.11/0.48 % Paramodulations : 4099
% 1.11/0.48 % Factorizations : 12
% 1.11/0.48 % NegExts : 0
% 1.11/0.48 % Equation resolutions : 157
% 1.11/0.48 % Disequality decompositions : 0
% 1.11/0.48 % Total rewrite steps : 1069
% 1.11/0.48 % ...of those cached : 836
% 1.11/0.48 % Propositional unsat checks : 0
% 1.11/0.48 % Propositional check models : 0
% 1.11/0.48 % Propositional check unsatisfiable : 0
% 1.11/0.48 % Propositional clauses : 0
% 1.11/0.48 % Propositional clauses after purity: 0
% 1.11/0.48 % Propositional unsat core size : 0
% 1.11/0.48 % Propositional preprocessing time : 0.000
% 1.11/0.48 % Propositional encoding time : 0.000
% 1.11/0.48 % Propositional solver time : 0.000
% 1.11/0.48 % Success case prop preproc time : 0.000
% 1.11/0.48 % Success case prop encoding time : 0.000
% 1.11/0.48 % Success case prop solver time : 0.000
% 1.11/0.48 % Current number of processed clauses : 380
% 1.11/0.48 % Positive orientable unit clauses : 43
% 1.11/0.48 % Positive unorientable unit clauses: 1
% 1.11/0.48 % Negative unit clauses : 25
% 1.11/0.48 % Non-unit-clauses : 311
% 1.11/0.48 % Current number of unprocessed clauses: 3405
% 1.11/0.48 % ...number of literals in the above : 11431
% 1.11/0.48 % Current number of archived formulas : 0
% 1.11/0.48 % Current number of archived clauses : 354
% 1.11/0.48 % Clause-clause subsumption calls (NU) : 34713
% 1.11/0.48 % Rec. Clause-clause subsumption calls : 21247
% 1.11/0.48 % Non-unit clause-clause subsumptions : 331
% 1.11/0.48 % Unit Clause-clause subsumption calls : 1194
% 1.11/0.48 % Rewrite failures with RHS unbound : 0
% 1.11/0.48 % BW rewrite match attempts : 26
% 1.11/0.48 % BW rewrite match successes : 10
% 1.11/0.48 % Condensation attempts : 1306
% 1.11/0.48 % Condensation successes : 28
% 1.11/0.48 % Termbank termtop insertions : 132303
% 1.11/0.48 % Search garbage collected termcells : 14211
% 1.11/0.48
% 1.11/0.48 % -------------------------------------------------
% 1.11/0.48 % User time : 0.151 s
% 1.11/0.48 % System time : 0.011 s
% 1.11/0.48 % Total time : 0.162 s
% 1.11/0.48 % Maximum resident set size: 6540 pages
% 1.11/0.48
% 1.11/0.48 % -------------------------------------------------
% 1.11/0.48 % User time : 0.536 s
% 1.11/0.48 % System time : 0.044 s
% 1.11/0.48 % Total time : 0.580 s
% 1.11/0.48 % Maximum resident set size: 5120 pages
% 1.11/0.48 % E exiting
%------------------------------------------------------------------------------